Sufficient conditions for monotonically constrained functional-type SIRMs connected fuzzy systems

Monotonic input-output relationship is common in many physical systems. When modeling a physical system whose input-output relationship is monotonic, it is desired for a model to have the monotonicity. In this paper, we construct a model with single input rule modules (SIRMs) connected fuzzy system to solve “the curse of dimensionality”, and propose sufficient conditions for the constructed fuzzy system to have monotonic input-output relationship. The conditions are obtained by restricting the first derivative of the fuzzy system to be nonnegative. The derived conditions can be classified into two parts: the condition on the consequent part parameters of fuzzy rules and the condition on the input membership functions. The simulation results show the validity of the derived conditions.